In machining a three-dimensional contour in a workpiece, it has been common to employ a rotary milling tool which in rotation provides at its axial end a rotating cutting surface. The rotating milling tool and the workpiece are brought into and held in substantial tangential contact while they are relatively displaced translationally in a predetermined three-dimensional coordinate system to progressively develop the machined contour in the workpiece. The path of translational relative displacement between the milling tool and the workpiece determines the eventual machined contour which is generally dissimilar in shape to the rotary cutting edge of the tool.
A desired three-dimensional contour which may be intricate in shape can also be produced in a workpiece by an electroerosion process. While to this end it has long been the common practice to employ a tool electrode with a preformed or machined shape complementary to the desired contour so that the tool electrode can be axially advanced to produce the desired machined contour in the workpiece, it has also been proposed to utilize a simple or "generic" electrode tool which is dissimilar in shape to the desired three-dimensional contour. In this latter case, as in the mechanical milling process, the electrode tool and the workpiece need to be relatively displaced translationally in a predetermined multi-axial coordinate system while they are held in a close proximity relationship across the machining gap flooded with an electroerosion fluid medium. The electrode tool may be either rotational or non-rotational.
In both the milling and electroerosion processes described, it is the prime interest of industry to achieve the required relative displacement between the tool and the workpiece automatically by having resort to a numerical control (NC) system. In NC systems, numerical values corresponding to desired positions of tools are stored on record media such as punched paper tapers, punched cards or magnetic tapes so that they can be used to control the operation automatically.
For the three-dimensional machining processes described to be achieved automatically under numerical control, there must be determined a certain fixed point in the tool for its controlled displacement relative to the workpiece. It is practically necessary to locate such a reference point on the axis of the tool, that is the rotary axis of a reference milling cutter, or the axis of a rotary electroerosion tool electrode or of a non-rotary axially symmetrical electroerosion tool electrode. It is beneficial for NC purposes that the rotating milling or electroerosion tool provides an effective machining surface which is symmetrical about the rotary axis and assumes a body of revolution. Likewise, a non-rotary electroerosion tool should practically be of a shape of body of revolution and axially be symmetrical so that the reference point can be located on the tool axis. Then, since the desired contour to be machined in the workpiece is known, a number of points to be successively followed by substantial tangential contact between the tool and the workpiece can, in a predetermined three-dimensional coordinate system, be prelocated on the desired contour and the three-dimensional-coordinates of each of the positions for the reference point on the tool axis corresponding to each tangential contact point can be calculated from the three-dimensional coordinates of the latter when the curvature of the machining surface on each such tangential contact point is known. In general, the curvature varies from point to point as a function of the distance between the reference point in the tool and the point of tangential contact on the tool machining surface.
Accordingly, after establishing in a given three-dimensional coordinate system a prescribed number of points lying on a given machining path which the effective machining surface of the tool needs to follow while maintaining its substantial tangential contact with the workpiece to progressively develop the desired contour therein, it has been the common practice in the prior NC machining art to entail, prior to the actual machining operation, the step of individually computing from the three-dimensional coordinates of each given point on the machining path, the three-dimensional coordinates of the corresponding position for the reference point on the tool axis whereupon the data for all the individually computed three-dimensional coordinates of the reference positions needs to be stored on a memory medium so that they can be reproduced in the actual machining operation for relatively displacing the tool and the workpiece along the prescribed machining path. It will be apparent that this pre-machining procedure is a complicated, time-consuming and laborious programming or preprogramming task. The difficulties become multiplied where two or more separate record storages (e.g. punched tapes) should be prepared as are most often necessary to machine the workpiece in rough and finish in a number of steps to reach the eventual precision and finished-surface contour. Where such multiple machining operations are required, respective independent steps of computation to obtain the three-dimensional coordinates of the reference point are necessary for separate tools which are similar but different in size and the computed coordinate data must be stored in separate record media (e.g. punched tapes).